image 10.22 Alternative model. Refer to Exercise 10.19. The number of tornadoes in 2004 is much larger than expected and the number in 2014 is much smaller than expected. In fact, most of the large positive and negative deviations occur later in time. This suggests there may not be constant variance. Because the response variable is a count, one can argue the variance is not constant (for example, see the Poisson distribution, page 329).

  1. (a) Take the natural logarithm of the count and refit the model. What is the least-squares regression line?

  2. (b) Check the residuals of this model. Does the linear regression model fit these data? Explain your answer.

  3. (c) When the response y is on the log scale, the slope approximates the percent change in y for a unit increase in x. Construct an approximate 95% confidence interval for the annual percent change.

  4. (d) Does this model also support the hypothesis that tornadoes have increased over time? Explain your answer.

  5. (e) Construct a prediction interval for the predicted number of tornadoes in 2015 and compare it with the interval from part (d) of Exercise 10.19. (Note: An approximate interval can be constructed by first obtaining a prediction interval for log y and then taking the antilog (inverse function of log) of each interval endpoint.)

  6. (f) Which of the two models (and prediction) do you prefer? Explain why.